TY  - BOOK
AU  - Blokh,Alexander M.
AU  - Fokkink,Robbert J.
AU  - Mayer,John C.
AU  - Mayer,John C.
AU  - Oversteegen,Lex G.
TI  - Fixed Point Theorems for Plane Continua with Applications
T2  - Memoirs of the American Mathematical Society
SN  - 9781470410049
AV  - QA329.9 -- .F594 2012eb 
U1  - 515/.39 
PY  - 2013///
CY  - Providence
PB  - American Mathematical Society
KW  - Fixed point theory
KW  - Electronic books
N1  - Intro -- Contents -- List of Figures -- Preface -- Chapter 1. Introduction -- Part  1 .  Basic Theory -- Chapter 2. Preliminaries and outline of Part 1 -- 2.1. Index -- 2.2. Variation -- 2.3. Classes of maps -- 2.4. Partitioning domains -- Chapter 3. Tools -- 3.1. Stability of Index -- 3.2. Index and variation for finite partitions -- 3.3. Locating arcs of negative variation -- 3.4. Crosscuts and bumping arcs -- 3.5. Index and Variation for Carathéodory Loops -- 3.6. Prime Ends -- 3.7. Oriented maps -- 3.8. Induced maps of prime ends -- Chapter 4. Partitions of domains in the sphere -- 4.1. Kulkarni-Pinkall Partitions -- 4.2. Hyperbolic foliation of simply connected domains -- 4.3. Schoenflies Theorem -- 4.4. Prime ends -- Part  2 .  Applications of Basic Theory -- Chapter 5. Description of main results of Part 2 -- 5.1. Outchannels -- 5.2. Fixed points in invariant continua -- 5.3. Fixed points in non-invariant continua -the case of dendrites -- 5.4. Fixed points in non-invariant continua -the planar case -- 5.5. The polynomial case -- Chapter 6. Outchannels and their properties -- 6.1. Outchannels -- 6.2. Uniqueness of the Outchannel -- Chapter 7. Fixed points -- 7.1. Fixed points in invariant continua -- 7.2. Dendrites -- 7.3. Non-invariant continua and positively oriented maps of the plane -- 7.4. Maps with isolated fixed points -- 7.5. Applications to complex dynamics -- Bibliography -- Index
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114171
ER  -